1. Field of the Invention
This invention relates to quantum computing, more specifically to the characterization and measurement of superconducting structures.
2. Description of Related Art
Qubits
A quantum bit or qubit is the building block of a quantum computer. The qubit is similar to a conventional binary bit in that it can be either 0 or 1. However, the analogous states of the qubit are referred to as |0> and |1>. These are called the basis states of the qubit. During quantum computation, the state of the qubit becomes a superposition of its basis states. This is very different from the conventional binary bit, and it means that the state of the qubit simultaneously has a nonzero first probability of occupying a first basis state |0> and a nonzero second probability of occupying a second basis state |1>. Qualitatively, one can characterize a superposition of basis states as the qubit being in both basis states at once. Mathematically, a superposition is represented in terms of the overall state of the qubit |Ψ>=α|0>+β|1>, where α and β are probability amplitudes having both real and imaginary components. When the state of the qubit is read out, the quantum nature of the qubit is temporarily lost and the superposition collapses to either |0> or |1>, thus regaining its similarity to a conventional bit. The state of the qubit after it collapses depends on the probability amplitudes α and β just before the readout operation occurs.
The superposition of the basis states of the qubit is one facet of the power harnessed by a quantum computer. In order to be useful, the qubit must be combined with other qubits in a quantum register, where the capacity for representing information grows exponentially with the number of qubits in the quantum register. The power and nature of the quantum computer is well known and described in the art. See, e.g., U.S. Pat. No. 5,768,297 to Shor, which is hereby incorporated by reference in its entirety.
The field of quantum computing remained theoretical until the late 1990s when several hardware proposals were introduced and tested. For a survey of the current physical systems from which qubits can be formed see Braunstein and Lo (eds.), 2001, Scalable Quantum Computers, Wiley-VCH Verlag GmbH, Berlin, which is hereby incorporated by reference in its entirety. There are many physical requirements in order to form a quantum computer. See DiVincenzo in Braunstein and Lo (eds.), 2001, Scalable Quantum Computers., but one is that the qubits must be well characterized physical systems. This requirement includes the need to map out the energy potential of qubits and the qubits eigenstates.
Many qubits are superconducting structures. A superconducting material has zero electrical resistance below critical levels of current, magnetic field and temperature. One form of superconducing qubit includes Josephson junctions. There are two classes of qubits that include Josephson junctions charge qubit and phase qubits. Phase and charge are canonically conjugated variables that are related by basic quantum principles. The division of the two classes of qubits that include Josephson junctions is outlined in Makhlin et al., 2001, Reviews of Modem Physics, 73, p. 357, which is hereby incorporated by reference in its entirety.
Double Well Potential
Systems useful for quantum computing can include a double well potential, as depicted in FIG. 8A. A double well potential, 80, shows the energy of a qubit versus the phase of the qubit. There are two metastable states correlated with two minima 82-1 and 82-2 . Each minima can include the energy spectrum (i.e. series of quantized energy levels) of a qubit. The basis states |0>and |1> are represented by the ground state energy levels of the system. An example of systems having a double well potential are superconducting Josephson phase qubits in which the basis states of the qubit coincide with the phase of the qubit. In a double well potential, the ground states correlate with the phase states +Δφ and −Δφ. Superconducting phase qubits are known in the art and are described in detail in U.S. Pat. No. 6,459,097 B1 to Zagoskin, and U.S. patent application Ser. No. 09/872,495 to Amin et al., filed June, 2001, each of which is incorporated by reference in their entirety.
Quantum Tunneling
In classical mechanics, for a particle occupying a ground state to move to another state (e.g., another ground state in a degenerate system), the particle must be given more energy than the potential barrier that separates the two states. However, if the particle is governed by quantum mechanics, it is possible for the particle to tunnel through the potential barrier separating the two states even when the particle does not have sufficient energy to pass over the potential barrier separating the two states. See, for example, Atkins, 1983, Molecular Quantum Mechanics, Oxford University Press, New York. Atkins explains that a particle (e.g., a Cooper pair) may be found inside a classically forbidden region (forbidden because the particle does not have sufficient energy to be in the region). Atkins calls this effect “penetration of the barrier” or “tunneling.” This type of microscopic quantum tunneling is known in the art and, for example, characterizes the Josephson effect across Josephson junctions, where Cooper pairs pass through a region of non-superconducting material via the process of quantum tunneling. In superconductors and many other systems, the same quantum mechanical behavior extends to the mesoscopic scale where mesoscopic properties of the system (made up in part by contribution from Cooper pairs) behave according to quantum mechanical rules and hence demonstrate quantum tunneling.
Characterization of Qubits
Characterization of the classical and quantum behavior of a qubit is needed for qubit engineering. Qubits can be governed by the rules of classical mechanics or quantum mechanics. When qubits are governed by the rules of classical mechanics, they are said to be behaving “classically.” Characterization of qubit when they are behaving classically helps to predict (calibrate) the quantum behavior of the qubit when it is governed by the rules of quantum mechanics. States of a qubit that are behaving classically are termed metastable states. Metastable states are local minima in the qubit's potential energy landscape. The state of the qubit behaving classically may be found in these local minima. If there is no thermal activation, the state of the qubit behaving will not change. Further, since the qubit is in a classical regime, it can not tunnel out of the local minima. Therefore the qubit remains in the local minima.
In order to effectively use qubits in a quantum computer, the tunneling rate of the qubit should be characterized. The appropriate characterization of this quantity can aid the engineering and development of various qubit designs. Certain Josephson junctions and junction networks that exhibit time reversal symmetry breaking are suited for quantum computing because of the existence of doubly degenerate ground states of persistent current. The states are degenerate but distinguishable through the existence of magnetic flux found in either “up” or “down” direction corresponding to the persistent current states. These currents can exist in system of junctions or at single Josephson junction. See Bocko et al., 1997, IEEE Transactions on Applied Superconductivity 7, 3638 and U.S. Pat. No. 6,459,097 B1, each of which is incorporated by reference in its entirety.
Recently, several superconducting qubits were tested. See Nakamura et al., 1999, Nature 398, pp. 786–788; Friedman et al., 2000, Nature 406, pp. 43–46; van der Wal et al., 2000, Science 290, pp. 773–777, each of which is incorporated by reference in their entireties. Measurement and characterization of these devices relied on the use of a dc SQUID. The use of such a SQUID for testing and characterization may have drawbacks, including the necessity for taking many measurements. The latter is a variant of microwave spectroscopy experiments that relied on a large number of measurements from which device characteristics can be statistically inferred. Data takes months to collect and therefore a more immediate and unobtrusive method for measurement and characterization of superconducting structures is needed.